http://www.google.com/url?sa=i&rct=j&q=extreme&source=images&cd=&cad=rja&docid=NOPIUBEUg45vKM&tbnid=QCaJ1GugvI8f3M:&ved=0CAUQjRw&url=http%3A%2F%2Fadventure.howstuffworks.com%2Foutdoor-activities%2Fsnow-sports%2Fextreme-skiing.htm&ei=OCCcUYG-Gq_D4AO9lICgCg&psig=AFQjCNEQWYVGO_NSnN2LcVYyUyjjwBvPjw&ust=1369272729541567

Step 1 – Order Numbers

Order the set of numbers from least to greatest.

Find the median. The median is the middle number. If the data has two middle numbers, find the mean of the two

numbers. What is the median?

Step 2 – Find the Median

Find the lower, or first quartile and upper, or third quartiles. These are considered the lower and upper medians. These are the middle numbers on each side

of the median. What are they in this example?

Step 3 – First & Third Quartiles

Interquartile Range

The interquartile range is the difference between the upper quartile and the lower quartile.

14 – 8.5 =5.5

Now you are ready to construct the actual box & whisker graph. First you will need to draw an ordinary number line that extends far enough in both directions to include all the numbers in your data:

Step 4 – Draw a Number Line

Locate the median using a vertical line just above your number line:

Step 5 – Draw the Parts

Locate the first quartile and the third quartile with similar vertical lines:

Step 5 – Draw the Parts

Next, draw a box using the lower and upper median lines as endpoints:

Step 5 – Draw the Parts

Finally, the whiskers extend out to the data's smallest number, 5 and largest number, 20:

Step 5 – Draw the Parts

Outliers are not included in the box and whisker plot. They are shown as an asterisks on the number line. For example, if the data set had an outlier of 24, it would

be show as seen below.

Step 6 - Label the Parts of a Box-and-Whisker Plot

1 23

54

Outliers are not included in the box and whisker plot. They are shown as an asterisks on the number line.

Median Third QuartileFirst Quartile

Lower extreme Upper extreme2

Lower Quartile = 5½

Q1

Upper Quartile = 9

Q3

Median = 8

Q2

4 5 6 7 8 9 10 11 12

4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12

Example 1: Draw a Box plot for the data below

Drawing a Box Plot.

Upper Quartile = 10

Q3

Lower Quartile = 4

Q1

Median = 8

Q2

3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15,

Example 2: Draw a Box plot for the data below

Drawing a Box Plot.

3 4 5 6 7 8 9 10 11 12 13 14 15

Upper Quartile = 180

Qu

Lower Quartile = 158

QL

Median = 171

Q2

Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data.

Drawing a Box Plot.

115, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186

130

140

150

160

170

180

190

cm

Practice

Use the following set of data to create a box plot.

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

Median

What is the median or 2nd quartile?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

The median is 39

1st Quartile

What is the 1st quartile?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

The lower quartile is 11

3rd Quartile

What is the 3rd quartile?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

The third quartile is 61

What is the Interquartile Range?

50

Outliers

An outlier is a number that falls outside the limits.

Are there any outliers?

The outlier is 220

Upper Extreme

What is the upper extreme?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

The upper extreme is 99

c

Lower Extreme

What is the lower extreme limit?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

The lower extreme is 3

Graphing The Data

Now use the data you have collected to create a box and whisker plot.

Independent Practice – Create box plots for the following data

12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10

Example 1: Draw a box plot for the data below.

6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10

Example 2: Draw a box plot for the data below.

Worksheet 1